Washington has slapped sanctions on President Nicolas Maduro and some of his allies, and branded him a "dictator" over his attempts to crush his country's opposition. Venezuela has in turn accused America of "imperialist aggression."
But Friday's latest comments were the first sign that Trump may be mulling military intervention.
"We have many options for Venezuela, including a possible military option if necessary," Trump told reporters in New Jersey.
"We have troops all over the world in places that are very far away. Venezuela is not very far away and the people are suffering and they're dying."
Trump said Venezuela's political crisis was among the topics discussed at the talks he hosted in New Jersey on Friday with Secretary of State Rex Tillerson and UN Ambassador Nikki Haley.
"Venezuela is a mess. It is very dangerous mess and a very sad situation," Trump said.
But if any US military contingency planning is under way, it must be in its early stages. A spokesman for the Department of Defense, Eric Pahon, refused to elaborate on Trump's comments, adding: "As of right now, the Pentagon has received no orders."
And the military command responsible for US operations in Latin America, Southern Command, said: "The military conducts contingency planning for a variety of situations.
"If called upon, we are prepared to support whole-of-government efforts to protect our national interest and safeguard US citizens. US Southern Command has not received an order."
Trump's warning came two days after his administration imposed new sanctions on Venezuela, targeting members of a loyalist assembly installed last week to bolster what Washington calls Maduro's "dictatorship".
The Venezuelan government responded to the sanctions -- which already targeted Maduro himself -- by saying the US was "making a fool of itself in front of the world."
On Thursday, Maduro declared that Venezuela's new Constituent Assembly holds supreme power over all branches of government, even over his position, and that its work -- ostensibly to rewrite the constitution -- would return "peace" to the country.
But the United States and major Latin American nations allege that Maduro is using the body as a tool to quash dissent, by clamping down on the opposition and the legislature it controls.
The crisis has fuelled the street demonstrations that have gripped Venezuela for the past four months. Nearly 130 people have been killed in clashes between protesters and security forces.
The protests have lost steam in the past week as security forces have stepped up repression and demonstrators have grown discouraged by the opposition's failure to bring about change.
But hackers have taken up the torch. On Thursday a group calling itself The Binary Guardians claimed responsibility for a massive cyberattack that cut mobile telephone service to seven million users.
Opposition to Maduro among the oil-exporting country's 30 million citizens increased during a long economic crisis that brought food shortages and hyperinflation to what was once of Latin America's wealthiest countries.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)